According to the CDC the proportion of all gonorrhea cases t

According to the CDC, the proportion of all gonorrhea cases tested in 2010 that were resistent to a major antibiotic was .27. A researcher takes an SRS of 50 medial records of patients diagnosed with gonorrhea in 2010 and records the proportion that had shown resistahnce to a major antibiotic. In an SRS of 50 medical cases, the probability of getting 25% or more cases that are resistence to a major antibiotic is?

Solution

Proportion ( P ) =0.27
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.27*0.73/50)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 0.25) = (0.25-0.27)/0.0628
= -0.02/0.0628= -0.3185
= P ( Z <-0.3185) From Standard Normal Table
= 0.3751                  
P( X>=0.25) = 1 - 0.3751 = 0.6249